Wild Soul (Arachnid) Vigilante seems very Spider-Man to me, gains some web abilities including the ability to move using them, you gain Uncanny Dodge/Improved(?) Uncanny Dodge and can still choose Avenger or Stalker Vigilante. Swings and round abouts on which to pick, but I’d probably go Stalker for the evasion and stealthy abilities but that is really a player choice. If third party is allowed, Path of War has a Greater Unarmed Strike feat which puts Unarmed Strike up to 1d8, then 1d10 at 10th level. There’s even a Light Armour from Armour Master’s Handbook called the Arachnid Harness which grants you a set of spider limbs you can use to climb with and which prevents you from losing your DEX modifier to AC whilst doing so.

Most seem to agree that Spider-Man will have some Monk levels. The Flowing Monk archetype seems to be the most suggested on another thread.

Honestly, Monk seems like a poor fit. The only real overlap is unarmed strikes, because Spider Man typically fights unarmed. Monks are way more than just unarmed fighters, though - those are Fighters who take Improved Unarmed Strike (or perhaps the Martial Artist archetype). Making other classes do unarmed combat well is another matter, sure, but theme-wise there's almost nothing else Monk-like about Spider Man. Ninja would be more fitting.

Which, in turn, means that Teisatsu Vigilante would be more fitting, because it's almost as good a Ninja as the Ninja (maybe better!) plus it's a Vigilante which is basically the masked superhero class. Actually, though, the Wild Soul is probably the best choice (though I don't recall if t's any good, mechanically).

In both cases one could easily argue that neither is mechanically efficient (it's tempting to house rule both classes), but those are obviously Pathfinder translations. I can cosign usability, as I'm currently GMing a Pathfinder Superhero game with Red She Hulk (interrupted more as standard She Hulk) and Ultimate Spiderman. My solutions were the Advanced template on RSH and giving each class feature a "level" earlier on all of the Wildsouls except Feline (so
Spidey gets Heighted Senses and Shoot Webs at 2nd, Web Specialist at 6th, and Web Master at 12th).

Also, I may have mentioned this, but one can make a decent Flash. Dip one level Relic Hunter Occultist (the speed force) for the Travel Domain, Expeditious Retreat spell, and the Sudden Speed base focus power. Next one level dip is Urban Bloodrager for the extra 10' base and increasing DEX. Fill the rest with your favorite monk flavor; I prefer Perfect Combat, since most of these guys are scientists. Toss in an elf with all FCBs going to speed and Long-Limbed, and you're looking at 45' base speed level one with a max of 105' (+30' for Sudden Speed and +30' for Expeditious Retreat), 55'/115' at level two, and then the monk's 70'/120' at level 5, increasing with monk's speed bonus. Boots of Striding help, but eventually get overshadowed by the monk speed bonus; this is also why he's topping out at 120'

Most seem to agree that Spider-Man will have some Monk levels. The Flowing Monk archetype seems to be the most suggested on another thread.

I know it's not going to be exact, but I'd like to get it as close as I can.

Some monk or ninja (or both) is critical.

I've got three different Spider-Man builds, all are Pathfinder, but all use some combination of Mythic levels, templates, and GM special allowances to even get close to Spider-Man's level of power. All three builds were using the Elephant in the Room no feat tax system, so that helped too. Depending on what your build constraints are they may or may not be useful for you. But I'm happy to walk you through them.

All of my builds sought to do some combination of the following: Spider sense (i.e. high initiative & act in surprise round), agility (high dex, high acrobatics/jumping, high AC), some mechanics to assist in quick costume changes, the Antagonize feat (custom made for Spider-Man!), wall climbing, charisma, alchemy skills, web-slinging (through a GM created artifact or early adoption of Wildsoul abilities) and unarmed combat ability.

My first build, for DrakeStryker's Superheroic Golarian Universe was Unchained Monk 2/Unchained Ninja 3. U Ninja is a 3rd party class, but very reasonably done, just bringing Ninja in line with the improvements made to U Rogue, not trying to be unbalanced. I went Oniwaban for the ninja to get some disguise ability (and to trade out the poison use). Then for the Monk side I went with Nornkith to act in the surprise round and stack up my monk abilities on CHA.

I was able to take the Advanced template to boost my abilities by +4 (which helps since Spider-Man is smart, strong, quick, charismatic and durable. Very MAD!). I got the Wall Climber ninja trick, and had a GM designed artifact (Gloves of the Spider-Web) that provided all my web ability. Branch Pounce looked like a fun, thematic feat to use.

A new GM took over the game and made me redo my character using Vigilante. The Wildsoul archetype was made with Spider-Man in mind, but it comes online so slow to make it worthless except for high level games. You don't even get a climb speed till level 12! Ahhh, a Ninja can do it at level 2. Anyhow, the GM let those abilities start earlier, so I was able to shoot webs at 2nd level instead of 6. The GM took away the custom artifact, but gave us Mythic levels instead. That's where I got wall climbing.

Since vigilante was already letting me act in the surprise round I switched my monk archetype to scaled fist. Not a great thematic fit, but gave me Dragon Style for free, which is nice. Dragon Style/Ferocity let me add up some nice damage, and with Enforcer & Hurtful I could get free demoralize & swift bonus attack after hitting someone with a nonlethal attack (which, as Spider-Man, I'd always be doing). The social talents are pretty useless for Peter Parker, but I added on some extra alchemy utility.

The GM said I was the heaviest hitter in the game and asked me to scale it back. So I made a third version. I ended up liking this one most of all. I switched from U Monk to standard Monk so I could go with Vigilante (Wildsoul) 4/Monk (Master of Many Styles/Kata Master) 1. This meant I couldn't dump WIS anymore, but with the ability score boosts from my three Mythic tiers I was able to get a 16 or higher in all my abilities. Going MoMM though got me the incredible Cloak & Dagger Style feat (and when I hit Monk 2, I'd get the even better Cloak & Dagger Subterfuge). Normally you need BAB 11 to get that, but a MoMM monk can get it at 2nd level, wow! Together those two feats let you make an AoO whenever an enemy removes a dirty trick condition, and in addition to the attack you can make a free dirty trick attempt AND a free steal attempt. So using the web as fluff for the dirty trick you can shoot webs in someone's eyes, or tangle them up, or do all sorts of other fun stuff to them and more or less incapacitate them in a very Spider-Manesque way.

Canny Tumble gives you +2 attack and makes your foe flat footed against you after tumbling through a threatened square. I went with a Stalker vigilante to get some hidden strike damage (1d4's vs. flat footed foes). With my +21 on acrobatics this was a very Spider-Man tactic of slipping past enemies and hitting them in a weak spot. Better yet with the vigilante talent Foe Collision, after I hidden strike an enemy I can also throw him into another adjacent foe. Fun & perfect!

I picked up the Kata Master archetype to trade Stunning Fist (not a great fit for Spider-Man) for panache (much better!). A Swordmaster's Flair gets some handy extra Swashbuckler Deeds. The last cool ability I had was the Deadly Dodge mythic ability. I could get +4 AC with a swift action and if an enemy missed me I could either make an AoO against them or redirect their attack to another enemy. More fun combat antics!

If I had kept playing in the game I would have wanted to add the Aerial Assault mythic ability to have really far reaching leaping attacks.

This third build didn't hit as hard as the second one (+12/ 1d6+6 vs. +14/ 1d6+11/+2d6), but was way more fun and versatile. Throwing enemies into each other, dirty tricks, redirecting attacks, lots of AoOs and movement. My one brief encounter with the character was pretty amazing. Anyhow, I hope this wall of text (and my linked to character sheets) is useful and interesting!

Ok, so I looked at Wildsoul Vigilante. The Arachnid abilities are very Spider-Man like. It's just too bad that they take so long to get online. Can't web-sling around until level 18 as a pure class. It does let him get the Stalker talent without being a stalker vigilante, which is nice. The Pirate Rogue archetype can move around in ropes and can use them to change direction for a charge. I can probably find an item to approximate web-slinging with this archetype. However it does remove Trap Sense so I would have to find a way to replace that. Also, the Flowing Monk archetype gives him to do an immediate trip attack if he's attacked by an opponent he's already threatening. If I start with Vigilante and be an avenger, at level two he can take the talent that gives the Improved Unarmed Attack. When and if I take a level in Flowing Monk, I can then retrain that talent for something else.

So that's starting off with at least 2 levels of Wildsoul Vigilante, followed by 2 levels of Pirate Rogue. I'd take a third level if the archetype didn't trade out Trap Sense, but it does. Then 2 levels of Flowing Monk, followed by more Vigilante levels. After a while, I might take 2 more levels of Monk to trip an opponent that's attacking an adjacent ally.

In another Pathfinder forum, someone mentioned the PrC Master Chymist. I looked it up and it's pretty perfect for Hulk. Seriously. The mutagen form has its own personality and alignment and can be used at will without having to drink the mutagen. Sometimes it'll even come out without permission if you're stressed.

It requires third level extracts and either the feral or infuse mutagen discoveries. So that's 7 levels of Alchemist to qualify. The feral mutagen discovery might be better for the first one taken. Yes, the Hulk uses fists and not claws, but it would save on having to take Improved Unarmed Strike if I don't want to. I could add a couple of Barbarian levels here and there for the rage powers.

For race, I was thinking either human or half-orc. Both have advantages and disadvantages.

So, I take the Feral Mutagen at Alchemist level 2. Before then, he'll use a Cetus to fight instead. And he'll keep the Cetus to fight with when the Mutagen effects run out. I get two more Discoveries before I can qualify for the PrC. I'm looking at Spontaneous Healing, Lingering Spirit, Pheromones, and Bone-Spike Mutagen.

For Barbarian rage powers, the best ones take need at least 6 levels, which kind of sucks. For the first one, I'm thinking either Intimidating Glare or Lesser Beast Totem. The first one lets me use Str instead of Cha for Intimidate while raging and can do it as a move action if the target is adjacent to me. The second nets claw attacks which I can use when the ones from the mutagen runs out.